Do I stay or leave my boyfriend who is controlling and has a split personality?

I feel like I’m at a breaking point with my boyfriend of 6 years. While I know we really love each other and he has some great qualities, he has a split personality. In particular, he can’t ever see anything wrong with himself and becomes very defensive and angry if anything is brought up. For example, he has almost no assets but is able to pay bills with working and social security but he is also almost retirement ago; yet, if I bring up that it makes me nervous how we would set up a household together if he runs short on money to help with the expenses, he totally disagrees and says he is doing “just fine”. Another example is that he can’t accept the consequences of a bank fraud crime he admitted to almost 15 years ago. So, when he applied to be a substitute teacher and they denied him b/c of this, he flipped out and said how unfair it was. A further example is one of my adult children doesn’t believe he is trustworthy and he yells at me and said I should tell that child he is totally trustworthy rather than saying the person may have that impression b/c of his past but he is very reliable and trustworthy since that time. He also can be arrogant (bragging about things). I realize I’m far from perfect but I am very financially settled and am moral (and as a result, have had a hard time being with him but fell in love anyway). I know that as we age, there will always be something with a prospective partner that we have to deal with but he seems to be narcissist/delusional sometimes while most other times he is very loving and compassionate. Should I run from him and give up

You ask us wether you should leave a person who can't take criticism, can't handle money, won't correct himself and is unrealistic? What would you do if I (a stranger on the internet) told you to stay? What would you do if I told you to run and give up? What would you to if I told you to not give up and not run away, but to think where you want to run to and which ways would lead there? Would you dare take a step?

In all honestly, he sounds very narcissistic and I wouldn't wish anyone to be in that kind of relationship. It sounds like you're going the extra mile for someone who thinks they are above you and life shouldn't be like that. Would you want your children to take advice/follow his footsteps?